Rob Underhill, the Underhill Society's genealogist, reviewed the question of Capt. John Underhill's birthdate and birthplace, and provided this information taken from Vol. VII of the Underhill Genealogy, compiled and edited by Carl J. Underhill and published in 2002.
Quote from the Foreward of this book written by Mr. Harry Macy, Jr. in June 2001.
"Captain John Underhill's Birthdate. Although Capt. John Underhill of New York appears in numerous records of his time until 1995 no record had been found which gave any clue as to his birthdate. Nineteenth-century Underhill family genealogists decided he probably was born about 1597, and someone dreamed up from this an exact birthdate of October 7, 1597....
In 1995 research at the Newport (R.I.) Historical Society disclosed, among some original court papers, a deposition made on 30 July 1655 by 'Captaine John Underhill aged about 46 years.' The document bears the Captain's well-known signature.... If he was age 46 in July 1655, Captain John was born in the latter half of 1608 or first half of 1609, when his mother was living at Bergen-op-Zoom in the Netherlands (it was previously assumed that he was born in England)."